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Distributivity and deformation of the reals from Tsallis entropy

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  • Kalogeropoulos, Nikos

Abstract

We propose a one-parameter family Rq of deformations of the reals, which is motivated by the generalized additivity of the Tsallis entropy. We introduce a generalized multiplication which is distributive with respect to the generalized addition of the Tsallis entropy. These operations establish a one-parameter family of field isomorphisms τq between R and Rq through which an absolute value on Rq is introduced. This turns out to be a quasisymmetric map, whose metric and measure-theoretical implications are pointed out.

Suggested Citation

  • Kalogeropoulos, Nikos, 2012. "Distributivity and deformation of the reals from Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1120-1127.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1120-1127
    DOI: 10.1016/j.physa.2011.11.023
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    Cited by:

    1. Nelson, Kenric P., 2015. "A definition of the coupled-product for multivariate coupled-exponentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 187-192.
    2. Nakamura, Gilberto M. & de Martini, Alexandre H. & Martinez, Alexandre S., 2019. "Extension of inverse q-Fourier transform via conformal mapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 106-111.

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